3 ms·
This is slightly interesting but I wonder what the median 3rd prime is, and 4th etc. Is there some sort of interesting pattern?
by lubujackson 3y ago
This is slightly interesting but I wonder what the median 3rd prime is, and 4th etc. Is there some sort of interesting pattern?
- madcaptenor 3y agoThey grow very quickly. The median third and fourth primes are 42719 and 5737850066077 - see https://oeis.org/A284411 https://oeis.org/A284411 . If p_k^* is the median kth prime then we have log log p_k^* = k - C + O(1/sqrt(k)) where C is a constant around 0.59483; that is, p_k^* grows like exp(exp(k)). This is "Corollaire 1.2" of the paper that the post links to (https://tenenb.perso.math.cnrs.fr/PPP/p_k%28n%29.pdf https://tenenb.perso.math.cnrs.fr/PPP/p_k%28n%29.pdf). (It's in French.)